{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OXJ5P22V26TUJFLRVVBGNACCBV","short_pith_number":"pith:OXJ5P22V","canonical_record":{"source":{"id":"1505.02597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-11T13:22:09Z","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"title_canon_sha256":"2b237ada84dbbaaed2fd43f943d60f0d6a6477af170a20d68ad28082402812be","abstract_canon_sha256":"6fdd61e70c78b473b6bb5b4d3c41f5057591898f7ace8d7b4d566e044e1db8b7"},"schema_version":"1.0"},"canonical_sha256":"75d3d7eb55d7a7449571ad426680420d7e94cc977ecef36e54f5cb2f6d4ac533","source":{"kind":"arxiv","id":"1505.02597","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02597","created_at":"2026-05-18T00:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02597v2","created_at":"2026-05-18T00:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02597","created_at":"2026-05-18T00:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"OXJ5P22V26TU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OXJ5P22V26TUJFLR","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OXJ5P22V","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OXJ5P22V26TUJFLRVVBGNACCBV","target":"record","payload":{"canonical_record":{"source":{"id":"1505.02597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-11T13:22:09Z","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"title_canon_sha256":"2b237ada84dbbaaed2fd43f943d60f0d6a6477af170a20d68ad28082402812be","abstract_canon_sha256":"6fdd61e70c78b473b6bb5b4d3c41f5057591898f7ace8d7b4d566e044e1db8b7"},"schema_version":"1.0"},"canonical_sha256":"75d3d7eb55d7a7449571ad426680420d7e94cc977ecef36e54f5cb2f6d4ac533","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:10.798915Z","signature_b64":"parnIFbT50hyq6W2jmTgjqvDefqsLbzOhBC1nRspHoNVujEuoJqNnuIH6WqkWeIkMHMQCMZhuGyJSN6OL3eeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75d3d7eb55d7a7449571ad426680420d7e94cc977ecef36e54f5cb2f6d4ac533","last_reissued_at":"2026-05-18T00:58:10.798273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:10.798273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.02597","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vtZ01xfWxBeuOWwBdHRH6YnKWy88H9z0PTt+WNRYRruaHlQoir6fDbPsgIHWD4BKVR+mVglQram3D0qL4MeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:13:22.487129Z"},"content_sha256":"9376d114ebbe7296618f7570654f2df8693f96e806df51494a37247f348292dc","schema_version":"1.0","event_id":"sha256:9376d114ebbe7296618f7570654f2df8693f96e806df51494a37247f348292dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OXJ5P22V26TUJFLRVVBGNACCBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Probabilistic existence results for separable codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Simon R. Blackburn","submitted_at":"2015-05-11T13:22:09Z","abstract_excerpt":"Separable codes were defined by Cheng and Miao in 2011, motivated by applications to the identification of pirates in a multimedia setting. Combinatorially, $\\overline{t}$-separable codes lie somewhere between $t$-frameproof and $(t-1)$-frameproof codes: all $t$-frameproof codes are $\\overline{t}$-separable, and all $\\overline{t}$-separable codes are $(t-1)$-frameproof. Results for frameproof codes show that (when $q$ is large) there are $q$-ary $\\overline{t}$-separable codes of length $n$ with approximately $q^{\\lceil n/t\\rceil}$ codewords, and that no $q$-ary $\\overline{t}$-separable codes o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02597","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a7ISU/Ck0Nqu4c4qFhjyZzFW0S72fH7oldVHNlPkXTuvwf0bQgQo+B9Xwyf0/swNw6SuK+Tk1cbnCnI4Wt1FBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:13:22.487509Z"},"content_sha256":"360347c3a7b39803a180c828b25d0ac9e9a8e022347b175d04396622511de85d","schema_version":"1.0","event_id":"sha256:360347c3a7b39803a180c828b25d0ac9e9a8e022347b175d04396622511de85d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OXJ5P22V26TUJFLRVVBGNACCBV/bundle.json","state_url":"https://pith.science/pith/OXJ5P22V26TUJFLRVVBGNACCBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OXJ5P22V26TUJFLRVVBGNACCBV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T23:13:22Z","links":{"resolver":"https://pith.science/pith/OXJ5P22V26TUJFLRVVBGNACCBV","bundle":"https://pith.science/pith/OXJ5P22V26TUJFLRVVBGNACCBV/bundle.json","state":"https://pith.science/pith/OXJ5P22V26TUJFLRVVBGNACCBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OXJ5P22V26TUJFLRVVBGNACCBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OXJ5P22V26TUJFLRVVBGNACCBV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6fdd61e70c78b473b6bb5b4d3c41f5057591898f7ace8d7b4d566e044e1db8b7","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-11T13:22:09Z","title_canon_sha256":"2b237ada84dbbaaed2fd43f943d60f0d6a6477af170a20d68ad28082402812be"},"schema_version":"1.0","source":{"id":"1505.02597","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02597","created_at":"2026-05-18T00:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02597v2","created_at":"2026-05-18T00:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02597","created_at":"2026-05-18T00:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"OXJ5P22V26TU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OXJ5P22V26TUJFLR","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OXJ5P22V","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:360347c3a7b39803a180c828b25d0ac9e9a8e022347b175d04396622511de85d","target":"graph","created_at":"2026-05-18T00:58:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Separable codes were defined by Cheng and Miao in 2011, motivated by applications to the identification of pirates in a multimedia setting. Combinatorially, $\\overline{t}$-separable codes lie somewhere between $t$-frameproof and $(t-1)$-frameproof codes: all $t$-frameproof codes are $\\overline{t}$-separable, and all $\\overline{t}$-separable codes are $(t-1)$-frameproof. Results for frameproof codes show that (when $q$ is large) there are $q$-ary $\\overline{t}$-separable codes of length $n$ with approximately $q^{\\lceil n/t\\rceil}$ codewords, and that no $q$-ary $\\overline{t}$-separable codes o","authors_text":"Simon R. Blackburn","cross_cats":["cs.DM","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-11T13:22:09Z","title":"Probabilistic existence results for separable codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02597","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9376d114ebbe7296618f7570654f2df8693f96e806df51494a37247f348292dc","target":"record","created_at":"2026-05-18T00:58:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6fdd61e70c78b473b6bb5b4d3c41f5057591898f7ace8d7b4d566e044e1db8b7","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-11T13:22:09Z","title_canon_sha256":"2b237ada84dbbaaed2fd43f943d60f0d6a6477af170a20d68ad28082402812be"},"schema_version":"1.0","source":{"id":"1505.02597","kind":"arxiv","version":2}},"canonical_sha256":"75d3d7eb55d7a7449571ad426680420d7e94cc977ecef36e54f5cb2f6d4ac533","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75d3d7eb55d7a7449571ad426680420d7e94cc977ecef36e54f5cb2f6d4ac533","first_computed_at":"2026-05-18T00:58:10.798273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:10.798273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"parnIFbT50hyq6W2jmTgjqvDefqsLbzOhBC1nRspHoNVujEuoJqNnuIH6WqkWeIkMHMQCMZhuGyJSN6OL3eeCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:10.798915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02597","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9376d114ebbe7296618f7570654f2df8693f96e806df51494a37247f348292dc","sha256:360347c3a7b39803a180c828b25d0ac9e9a8e022347b175d04396622511de85d"],"state_sha256":"7c877c6627adf57750b20b4a9a4b1999c8f924bbe6cef8db3daff717fd353db0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qm1ZKdP45O26CVrjipUCCy+UjknzqdSPMPaaVbxpY/XigZZ/lbxprCo3olsA435xG4hq5iRtOJwSX6ilZJEvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:13:22.489775Z","bundle_sha256":"08ea18365fa4612fb5a76cff90bd334ea8e13618aea5a84a510f1a5902e4ca27"}}